Ken helps Dan who goes on vacation for 10 days.Ken has 2 payment options.Choice 1:get 10 cents on day 1, 20 on 2, 40 on 3, 80 on 4 etc.Choice 2:get $75 immediately.Which option can get him more money?

Answer 1

This question is similar to solving for compounding interest. You have a starting value ($0.10) and you will double that every day for 10 days.

PV x Growth raised to the # of days = FV --->

0.10 x (2¹⁰) = 0.1 x 1024 = ___________

If that number is greater than $75 you want to select choice 1.

Answer 2

Stick with #1. The sum is $102.30.

Answer 3

The key words here are cents and dollars.

It seems like in Option two, Ken just gets $75 immediately, and that's it. Over ten days, that's $7.5 dollars per day.

In Option 1:

With each day, Ken gets 20 more cents. We can model this relationship with the following equation:

daily income in cents = 20x where x is the number of the day.

We know that Dan is on vacay for 10 days, so Ken will be working for ten days.On the tenth day (which will be the most he can make), he will make 10 x 20 cents = 200 cents, or $2.

Even if you add in all the previous days' earnings with option 1, it will not exceed the 75 Dollars from option 2, so he should go with option 2.